112 Frequently Asked Questions In Quantitative Finance
neutralstrategy. This means buying or selling more
options, not just the underlying.
Theta The theta,, is the rate of change of the option
price with time.
=
∂V
∂t
.
The theta is related to the option value, the delta and
the gamma by the Black--Scholes equation.
Speed The speed of an option is the rate of change of
the gamma with respect to the stock price.
Speed=
∂^3 V
∂S^3
.
Traders use the gamma to estimate how much they will
have to rehedge by if the stock moves. The stock moves
by $1 so the delta changes by whatever the gamma is.
But that’s only an approximation. The delta may change
by more or less than this, especially if the stock moves
by a larger amount, or the option is close to the strike
and expiration. Hence the use of speed in a higher-order
Taylor series expansion.
Vega The vega, sometimes known as zeta or kappa,
is a very important but confusing quantity. It is the
sensitivity of the option price to volatility.
Vega=
∂V
∂σ
.
This is completely different from the other greeks since
it is a derivative with respect to aparameterand not a
variable. This can be important. It is perfectly accept-
able to consider sensitivity to a variable, which does
vary, after all. However, it can be dangerous to measure
sensitivity to something, such as volatility, which is a
